Question

∠1 and ∠2 are vertical angles. if $m\angle 1 = (8x - 10)\degree$ and $m\angle 2 = (5x + 2)\degree$, then find the value o

Explanation:

Step1: 回忆对顶角性质

对顶角相等，所以\(m\angle1 = m\angle2\)，即\(8x - 10 = 5x + 2\)。

Step2: 解方程求\(x\)

移项可得\(8x - 5x = 2 + 10\)，即\(3x = 12\)，两边同时除以\(3\)，得\(x = \frac{12}{3} = 4\)。

Step3: 求角的度数（假设求\(m\angle1\)或\(m\angle2\)，这里以\(m\angle1\)为例）

将\(x = 4\)代入\(m\angle1 = (8x - 10)^{\circ}\)，得\(m\angle1 = 8\times4 - 10 = 32 - 10 = 22^{\circ}\)，同理\(m\angle2 = 5\times4 + 2 = 20 + 2 = 22^{\circ}\)。

Answer:

\(x = 4\)，\(m\angle1 = m\angle2 = 22^{\circ}\)（如果问题是求\(x\)和角的度数，根据题目未显示完整部分推测，若仅求\(x\)则为\(x = 4\)）